Triangles are defined by their angles, and the angle measures uniquely determine the triangle shape. In this case, the angles of the triangle are 80º, 80º, and 40º.
Since all triangles with the same set of angles are similar, and given that these angles satisfy the triangle angle sum theorem (which states that the sum of the angles in a triangle must equal 180º), there can only be one unique triangle shape that can be formed with these angles.
Thus, the correct response is:
one